Question

applying the converse of the side - splitter theorem which value of x would make \\( \overline { lk } \parallel \overline { om } \\)? ( x = 2 ) ( x = 2.4 ) ( x = 4.8 ) ( x = 8 )

Explanation:

Step1: Apply the Converse of the Side - Splitter Theorem

According to the Converse of the Side - Splitter Theorem, if \(\frac{NL}{LO}=\frac{MK}{KO}\), then \(LK\parallel OM\). Here, \(NL = x\), \(LO=x - 4\), \(MK=x - 3\), and \(KN=x + 2\). So we have the proportion \(\frac{x}{x - 4}=\frac{x + 2}{x-3}\).

Step2: Cross - multiply

Cross - multiplying gives us \(x(x - 3)=(x + 2)(x - 4)\).
Expand both sides:

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Step3: Solve for \(x\)

Subtract \(x^{2}\) from both sides of the equation \(x^{2}-3x=x^{2}-2x - 8\). We get \(-3x=-2x - 8\).
Add \(2x\) to both sides: \(-3x+2x=-2x - 8+2x\), which simplifies to \(-x=-8\).
Multiply both sides by \(- 1\) to get \(x = 8\).

Answer:

\(x = 8\) (the fourth option)